Working with Probabilities
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Working with Probabilities Physics 115a (Slideshow 1) A. Albrecht PowerPoint PPT Presentation


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Working with Probabilities Physics 115a (Slideshow 1) A. Albrecht These slides related to Griffiths section 1.3. Consider the following group of people in a room:. Histogram Form. Consider the following group of people in a room:. Total people = 14.

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Working with Probabilities Physics 115a (Slideshow 1) A. Albrecht

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Working with Probabilities

Physics 115a (Slideshow 1)

A. Albrecht

These slides related to Griffiths section 1.3


Consider the following group of people in a room:


Histogram Form


Consider the following group of people in a room:

Total people = 14


Consider the following group of people in a room:

Total people = 14


Consider the following group of people in a room:

Total people = 14


Consider the following group of people in a room:

Total people = 14


Consider the following group of people in a room:

Total people = 14


Consider the following group of people in a room:

Total people = 14


Consider the following group of people in a room:

Total people = 14


Probability Histogram


Number Histogram


NB: The probabilities for ages not listed are all zero

Total people = 14


Assuming Age<20, what is the probability of finding each age?

Total people = 14


Assuming Age<20, what is the probability of finding each age?

Total people = 14


Assuming Age<20, what is the probability of finding each age?

Total people = 14


Assuming no age constraint, what is the probability of finding each age?

Related to collapse of the waveunction (“changing the question”)

Total people = 14


Assuming Age<20, what is the probability of finding each age?

Related to collapse of the waveunction (“changing the question”)

Total people = 14


Consider a different room with different people:

Total people = 15


Consider a different room with different people:

Total people = 15


Red Room Numbers


Red Room Probabilities


Combine Red and Blue rooms

Total people = 29


  • Lessons so far

  • A simple application of probabilities

  • Normalization

  • “Re-Normalization” to answer a different question

  • Adding two “systems”.

  • All of the above are straightforward applications of intuition.


Expectation Values


Most probable answer = 25

Median = 23

Average = 21


Most probable answer = 25

Median = 23

Average = 21

Lesson: Lots of different types of questions (some quite similar) with different answers. Details depend on the full probability distribution.


Average (mean):

  • Standard QM notation

  • Called “expectation value”

  • NB in general (including the above) the “expectation value” need not even be possible outcome.


Average (number squared)


Careful: In general

In general, the average (or expectation value) of some function f(j) is


The “width” of a probability distribution


Discuss eqns 1.10 through 1.13 at board


Continuous Variables


Continuous Variables

Why not measure age in weeks?


Blue room in weeks


Blue room in weeks


Conclusion: Blue room in weeks not very useful/intuitive


Another case where a measure of age in weeks might by useful:

The ages of students taking health in the 8th grade in a large school district (3000 students).


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